Heat the oven to 350 F.
Heat the olive oil and 3 tablespoons of the butter in a large, deep skillet or Dutch oven over medium-high heat. Add the onions and cook until they start to brown, stirring often, about 10 minutes.
Add the mushrooms, chestnuts, and garlic, and stir well. Lower the heat to medium and cook until the mushrooms have released their water and the vegetables are fragrant and dark, about 10 minutes. Add the apples, celery, and herbs. Season with salt and a few grinds of black pepper, and cook for another 5 minutes, until the apples have softened slightly.
Place the diced bread in a large mixing bowl and add the cooked apple and vegetable mixture. Pour in the stock and stir to combine. Taste and season again with salt and pepper.
Grease the sides and bottom of the skillet with 1 tablespoon of butter. Pack the stuffing into the skillet, then break the remaining 3 tablespoons butter into pieces and dot them over the top. Cover with parchment paper, and top with a lid or foil. Bake for 30 minutes, then remove the cover and place under the broiler for 5-10 minutes, or until the top of the stuffing is crisp and browned at the edges. Serve hot.